Answer:
Option C could be the side lengths of a right triangle
Step-by-step explanation:
A) 60 in, 96 in, 120 in
Longest side = hypotenuse = 120 inch
To check measurements could be the side lengths of a right triangle
We will use Pythagoras theorem :
![Hypotenuse^2=Perpendicular^2+Base^2\\120^2=60^2+96^2\\14400 \neq 12816](https://tex.z-dn.net/?f=Hypotenuse%5E2%3DPerpendicular%5E2%2BBase%5E2%5C%5C120%5E2%3D60%5E2%2B96%5E2%5C%5C14400%20%5Cneq%2012816)
So, It is not a right angled triangle
B)72 in, 108 in, 120 in
Longest side = hypotenuse = 120 inch
To check measurements could be the side lengths of a right triangle
We will use Pythagoras theorem :
![Hypotenuse^2=Perpendicular^2+Base^2\\120^2=72^2+108^2\\14400 \neq 16848](https://tex.z-dn.net/?f=Hypotenuse%5E2%3DPerpendicular%5E2%2BBase%5E2%5C%5C120%5E2%3D72%5E2%2B108%5E2%5C%5C14400%20%5Cneq%2016848)
So, It is not a right angled triangle
C)72 in, 96 in 120
Longest side = hypotenuse = 120 inch
To check measurements could be the side lengths of a right triangle
We will use Pythagoras theorem :
![Hypotenuse^2=Perpendicular^2+Base^2\\120^2=72^2+96^2\\14400 =14400](https://tex.z-dn.net/?f=Hypotenuse%5E2%3DPerpendicular%5E2%2BBase%5E2%5C%5C120%5E2%3D72%5E2%2B96%5E2%5C%5C14400%20%3D14400)
So, It is a right angled triangle
D) 72 in, 96 in, 144 in
Longest side = hypotenuse = 144 inch
To check measurements could be the side lengths of a right triangle
We will use Pythagoras theorem :
![Hypotenuse^2=Perpendicular^2+Base^2\\144^2=72^2+96^2\\20736 \neq 14400](https://tex.z-dn.net/?f=Hypotenuse%5E2%3DPerpendicular%5E2%2BBase%5E2%5C%5C144%5E2%3D72%5E2%2B96%5E2%5C%5C20736%20%5Cneq%2014400)
So, It is a not right angled triangle
So, Option C could be the side lengths of a right triangle